Fuzzy Dominance Relation Rough Set Model For Interval-valued Information Systems

As a generalized form of single valued information system,interval valued information system can reflect the uncertainty of information.In practical application,because of technical conditions or human factors,information always is incomplete.Therefore,the study of complete and incomplete interval valued information systems is imperative.In this paper,we study fuzzy dominance relation rough set model for interval valued information systems.The main content of this paper can be summarized as follows:1.Interval ordered information systems are special interval-valued information systems,which have partial order relation on feature values.In this paper,we propose a fuzzy dominance relation for interval ordered information systems,and extend the fuzzy rank information entropy and the fuzzy rank mutual information to evaluate the importance of the feature.Consequently,an unsupervised feature selection method by combining a criterion,called UmIMR(Unsupervised maximum information and minimum redundancy),which takes into account both the amount of information and redundancy is proposed.The classification and clustering experimental results demonstrate the effectiveness of the proposed method.2.For incomplete interval valued information systems,a rough set method based on fuzzy dominance relation is constructed.The fuzzy dominance relation in which aims to describe the degree of dominance in terms of pairs of objects is proposed.Based on the relation,we extend the definitions of fuzzy approximation operators and investigate the uncertainty measurement problem,including accuracy,roughness,approximation accuracy,fuzzy entropy and so on.Also,a new fuzzy conditional entropy is used as a criterion to measure the importance of attributes.Then a corresponding heuristic attribute reduction algorithm is constructed for incomplete interval-valued decision systems.Experiments show that the fuzzy conditional entropy is a reasonable uncertainty measure,which can be applied to our attribute reduction approach.